2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110124Consider a random graph G in G(n,p) and the graph property: G contains a copy of a specific graph H. (Note: H depends on n; a motivating example: H is a Hamiltonian cycle.) Let q be the minimal value for which the expected number of copies of H' in G is at least 1/2 for every subgraph H' of H. Let p be the value for which the probability that G contains a copy of H is 1/2. Conjecture: p/q = O(log n). Related conjectures for general Boolean functions, and a possible connection with discrete isoperimetry are discussed.The gap between expectations and reality is studied, 7 pagesCombinatoricsProbability05C80, 05D40, 60C05, 60K35, 82B26, 94C10, 06E30text